In a typical project portfolio optimization problem, the decision makers would choose the optimal project portfolio from the candidates under the constraints of certain resources. However, in lots of real world examples, traditional approaches cannot perfectly solve the project portfolio optimization problems with unknown information about the importance of attributes. An innovative feature of this paper is to propose a stochastic multiattribute acceptability analysis (SMAA) to solve the multiattribute project portfolio optimization problems. SMAA includes a series of methods, which provide full ranks for a set of alternatives by exploring the weight space to make each alternative the most preferred one. Our proposed method provides feasible procedures to deal with the project portfolio optimization problems and, as an extension of traditional SMAA methods, expands the SMAA applications from the comparison of single alternatives to the comparison of sets of alternatives.